Nearby Cycles of Automorphic Étale Sheaves, II

2018 ◽  
pp. 83-106 ◽  
Author(s):  
Kai-Wen Lan ◽  
Benoît Stroh
Keyword(s):  
Nearby Cycles

scholarly journals The big projective module as a nearby cycles sheaf

2016 ◽  
Vol 23 (1) ◽  
pp. 721-726 ◽  
Author(s):  
Justin Campbell
Keyword(s):  
Projective Module ◽  
Nearby Cycles

scholarly journals Duality and nearby cycles over general bases

2019 ◽  
Vol 168 (16) ◽  
pp. 3135-3213
Author(s):  
Qing Lu ◽  
Weizhe Zheng
Keyword(s):  
Nearby Cycles

scholarly journals Local models for Weil-restricted groups

2016 ◽  
Vol 152 (12) ◽  
pp. 2563-2601 ◽  
Author(s):  
Brandon Levin
Keyword(s):  
Hecke Algebra ◽  
Shimura Varieties ◽  
Reductive Groups ◽  
Local Models ◽  
Central Function ◽  
Nearby Cycles ◽  
Weil Restriction ◽  
Trace Of Frobenius ◽  
Invent Math

We extend the group-theoretic construction of local models of Pappas and Zhu [Local models of Shimura varieties and a conjecture of Kottwitz, Invent. Math.194(2013), 147–254] to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive groups when$p\geqslant 5$. We show that the local models are normal with special fiber reduced and study the monodromy action on the sheaves of nearby cycles. As a consequence, we prove a conjecture of Kottwitz that the semi-simple trace of Frobenius gives a central function in the parahoric Hecke algebra. We also introduce a notion of splitting model and use this to study the inertial action in the case of an unramified group.

Nearby cycles of automorphic étale sheaves

2017 ◽  
Vol 154 (1) ◽  
pp. 80-119 ◽  
Author(s):  
Kai-Wen Lan ◽  
Benoît Stroh
Keyword(s):  
Characteristic Zero ◽  
Shimura Variety ◽  
Etale Cohomology ◽  
Nearby Cycles ◽  
Étale Cohomology

We show that the automorphic étale cohomology of a (possibly noncompact) PEL-type or Hodge-type Shimura variety in characteristic zero is canonically isomorphic to the cohomology of the associated nearby cycles over most of their mixed characteristics models constructed in the literature.

Nearby motives and motivic nearby cycles

2012 ◽  
Vol 19 (4) ◽  
pp. 879-902 ◽  
Author(s):  
Florian Ivorra ◽  
Julien Sebag
Keyword(s):  
Nearby Cycles
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